On the Secular Behavior of Irregular Satellites

Although analytical studies on the secular motion of the irregular satellites have been published recently (Kinoshita & Nakai 1999; Yokoyama et al. 2003), these theories have not yet been satisfactorily reconciled with the results of direct numerical integrations (Carruba et al. 2002; Nesvorný et al. 2003). These discrepancies occur because in secular theories the disturbing function is generally averaged over the Sun’s orbital motion, whereas instead one should take into account some periodic terms, most notably the so-called “evection”, which can be large for distant, slow-moving satellites. This problem is identical to that initially encountered by Newton and other historical researchers when studying the Moon’s motion. Here we demonstrate that the evection and other terms from lunar theory can be incorporated into the more modern Kozai formalism, and that our synthetic approach produces much better agreement with results from symplectic integrations. Using this method, we plot the locations of secular resonances in the orbital-element space inhabited by the irregular satellites. Our model is found to predict correctly those satellites that are resonant or nearresonant. We also analyze the octupole term in the disturbing function (Yokoyama et al. 2003) to determine the strengths of resonant-locking for satellites whose longitudes of pericenter are librating. By independently integrating these satellites’ nominal orbits using a symplectic integrator, we show that the strength of this resonance can be successfully obtained from simple analytical arguments. We note that the distribution of irregular satellite clusters in the space of proper orbital elements appears to be non-random. We find that the large majority of irregular-satellite groups cluster close to the secular resonances, with Department of Theoretical & Applied Mechanics, Cornell University, Ithaca, NY 14853